Magnetic resonance imaging (MRI) involves the transmission and receipt of radio frequency (RF) energy. RF energy may be transmitted by a coil. Resulting magnetic resonance (MR) signals may also be received by a coil. In early MRI, RF energy may have been transmitted from a single coil and resulting MR signals received by a single coil. Later, multiple receivers may have been used in parallel acquisition techniques. Similarly, multiple transmitters may have been used in parallel transmission techniques.
RF coils create the B1 field that rotates the net magnetization in a pulse sequence. RF coils may also detect processing transverse magnetization. Thus, RF coils may be transmit coils, receive coils, or transmit and receive coils. An imaging coil needs to be able to resonate at a selected Larmor frequency. Imaging coils include inductive elements and capacitive elements. Conventionally, the inductive elements and capacitive elements have been implemented using two terminal passive components (e.g., capacitors). The resonant frequency, v, of an RF coil is determined by the inductance (L) and capacitance (C) of the inductor capacitor circuit according to:
  v  =      1          2      ⁢      Π      ⁢              LC            
Imaging coils may need to be tuned. Tuning an imaging coil may include varying the performance of a capacitor. Recall that frequency: f=ω/(2π), wavelength: λ=c/f, and λ=4.7 m at 1.5 T. Recall also that the Larmor frequency: f0=γB0/(2π), where γ/(2π)=42.58 MHz/T; at 1.5 T, f0=63.87 MHz; at 3 T, f0=127.73 MHz; at 7 T, f0=298.06 MHz. Basic circuit design principles include the fact that capacitors add in parallel (impedance 1/(jCω)) and inductors add in series (impedance jLω).
There are many design issues associated with MRI RF coil design. For example, the inductance of a conventional coil depends on the geometry of the coil. For a square coil with a side length a and wire diameter f: L=[μ0/π] [−4a+2a √2−2a log(1+√2)+2a log(4a/f)]. For a loop coil with loop diameter d and wire diameter f: L=[μ0d/2] [ log(8d/f)−2]. Thus, the selection of the geometry of a coil determines, at least in part, the inductance of the coil.
The resistance of a coil also depends on the geometry of the coil. The resistance R of a conductor of length I and cross-sectional area A is R=μl/A, where ρ is the conductor resistivity and is a property of the conductor material and the temperature. For a copper wire coil with loop diameter d and wire diameter f: R=dρCu/(fδCu). For a copper foil coil with loop diameter d, copper thickness t, and copper width w: R=πdρCu/(2wδCu), where t is much greater than the copper skin depth and w is much greater than t. Thus, the selection of the geometry of a coil and the material (e.g., wire, foil) determines, at least in part, the inductance of the coil. The length of the loop also impacts the properties of the coil.
Coils may be characterized by their signal voltage, which is the electro-motive force (emf) induced in a coil: ξ=−∂φ/∂t∝−∂(B1˜M0)/∂t, where φ is the magnetic flux across the coil (closed loop), magnetization M0=Nγ2(h/(2π)2s(s+1)B0/(3kBTS)=σ0B0/μ0, where N is the number of nuclear spins s per unit volume (s=½ for protons) and TS is the temperature of the sample. Since θ0=γB0, ξ∝ω02. The noise in a coil may be thermal (e.g., v=(4kBTSRΔf)1/2, where R is the total resistance and Δf is the bandwidth of the received signal). The signal to noise ratio (SNR) for a coil may be described by ξ/v.
Coils may be used for transmitting RF energy that is intended to cause nuclear magnetic resonance (NMR) in a sample. The frequency at which NMR will be created depends on the magnetic field present in the sample. Both the main magnetic field B0 produced by the MRI apparatus and the additional magnetic field B1 produced by a coil contribute to the magnetic field present in the sample. For a circular loop coil, the transmit B1 field equals the coil sensitivity. A circular loop of radius a carrying a current I produces on axis the field: B=μ0/a2/[2(a2+z2)3/2].
Additionally, RF coils for MRI may need to be tuned and matched. Tuning involves establishing or manipulating the capacitance in a coil so that a desired resistance is produced. Matching involves establishing or manipulating the capacitance in a coil so that a desired reactance is achieved. When tuning, the impedance z may be described by Z=R+jX=1/(1/(r+jLω)+jCω). Tuning may be performed to achieve a desired tuning frequency for a coil. ω0 identifies the desired tuning frequency. ω0, may be, for example, 63.87 MHz at 1.5 T. The size of a conventional coil facilitates estimating inductance L. With an estimate of L in hand, values for capacitors can be computed to produce a desired resonant peak in an appropriate location with respect to ω0. Once capacitors are selected, the resonant peak can be observed and a more accurate L can be computed. The capacitors can then be adjusted to produce the desired resistance. Once the desired resistance is achieved, then capacitance can be adjusted to cancel reactance.
There are a number of complicated design issues associated with conventional RF coils. Conventional coil design involves selecting and manipulating capacitors. The selection and manipulation depends on many factors including coil material (e.g., foil, wire), coil geometry (e.g., square, loop), fabrication technique (e.g., surface mount, etched onto printed circuit board) and other choices. Coil design is further complicated by the fact that splitting a coil with capacitors may affect radiation losses, dielectric losses, resistance, and fabrication issues (e.g., additional soldering).
Conventional coils may use PIN diodes. When forward-biased, a PIN diode may produce a negligible resistance (e.g., 0.1Ω), which is essentially a short-circuit. When reverse-biased, a PIN diode may produce a high resistance (e.g., 200 kΩ) in parallel with a low capacitance (e.g., ˜2 pF), which is essentially an open-circuit. Conventional coils may also be designed with a single element or two or more elements. The number of elements may affect the properties of the coil. Additionally, the size, width, and material of the conductor may affect the properties of the coil.
Thus, conventional coil design may be a complicated process that requires numerous decisions. Additionally, conventional coil fabrication may be a complicated process that requires accurately implementing manufactures that reflect the design decisions. Simpler and less costly approaches are constantly sought.
Prior Art FIG. 1 illustrates a schematic of a simple conventional RF coil 100 for MRI. The coil 100 is illustrated as a loop 110. Loop 110 has elements that produce a resistance (e.g., resistor 120) and that produce an inductance (e.g., inductor 130). A conventional loop may include a matching capacitor 140 and tuning capacitor 150. Conventionally, the resistor 120, inductor 130, and capacitor 150 may all have been two terminal passive elements that were soldered to copper wire or copper foil that was attached to a printed circuit board.
A resistor may be, for example, a passive, two-terminal electrical component that implements electrical resistance as a circuit element. Resistors reduce current flow. Resistors also lower voltage levels within circuits. Resistors may have fixed resistances or variable resistances. The current that flows through a resistor is directly proportional to the voltage applied across the resistor's terminals. This relationship is represented by Ohm's Law: V=IR, where I is the current through the conductor, V is the potential difference across the conductor, and R is the resistance of the conductor.
An inductor, which may also be referred to as a coil or reactor, may be a passive two-terminal electrical component that resists changes in electric current. An inductor may be made from, for example, a wire that is wound into a coil. When a current flows through the inductor, energy may be stored temporarily in a magnetic field in the coil. When the current flowing through the inductor changes, the time-varying magnetic field induces a voltage in the inductor. The voltage will be induced according to Faraday's law and thus may oppose the change in current that created the voltage.
A capacitor may be a passive, two-terminal electrical component that is used to store energy. The energy may be stored electrostatically in an electric field. Although there are many types of practical capacitors, capacitors tend to contain at least two electrical conductors that are separated by a dielectric. The conductors may be, for example, plates and the dielectric may be, for example, an insulator. The conductors may be, for example, thin films of metal, aluminum foil or other materials. The non-conducting dielectric increases the capacitor's charge capacity. The dielectric may be, for example, glass, ceramic, plastic film, air, paper, mica, or other materials. Unlike a resistor, a capacitor does not dissipate energy. Instead, a capacitor stores energy in the form of an electrostatic field between its conductors.
When there is a potential difference across the conductors, an electric field may develop across the dielectric. The electric field may cause positive charge (+Q) to collect on one conductor and negative charge (−Q) to collect on the other conductor.
Prior Art FIG. 2 illustrates a schematic of another simple RF coil 200 for MRI. The coil 200 is illustrated as a square loop 210. Loop 210 has elements that produce a resistance (e.g., resistor 220) and that produce an inductance (e.g., inductor 230). A conventional loop may include a capacitor 240 and capacitor 250 that work together to achieve matching. Once again, the resistor 220, inductor 230, and capacitors 240 and 250 may have been soldered to copper wire or copper foil that was attached to a printed circuit board. Coil 200 is contrasted with coil 1 (Prior Art FIG. 1) that included capacitor 150 for tuning purposes.
Prior Art FIG. 3 illustrates a cross-section of a conventional coaxial (“coax”) cable 300. Cable 300 includes an inner conductor 310 which may be, for example, a copper wire. Cable 300 also includes an outer conductor 330 which may be, for example, a copper mesh. A dielectric spacer 320 may reside between the inner conductor 310 and the outer conductor 330. The cable 300 may be protected by an outer cover 340.